Algebra Examples

$- x + y + - 5 x + y = 5$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

$- x + y - 5 x + y = 5$

Step 2

Simplify $- x + y + - 5 x + y$ .

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Step 2.1

Subtract $5 x$ from $- x$ .

$- 6 x + y + y = 5$

Step 2.2

Add $y$ and $y$ .

$- 6 x + 2 y = 5$

Step 3

Subtract $2 y$ from both sides of the equation.

$- 6 x = 5 - 2 y$

Step 4

Divide each term in $- 6 x = 5 - 2 y$ by $- 6$ and simplify.

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Step 4.1

Divide each term in $- 6 x = 5 - 2 y$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{5}{- 6} + \frac{- 2 y}{- 6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{5}{- 6} + \frac{- 2 y}{- 6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{- 6} + \frac{- 2 y}{- 6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Move the negative in front of the fraction.

$x = - \frac{5}{6} + \frac{- 2 y}{- 6}$

Step 4.3.1.2

Cancel the common factor of $- 2$ and $- 6$ .

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Step 4.3.1.2.1

Factor $- 2$ out of $- 2 y$ .

$x = - \frac{5}{6} + \frac{- 2 (y)}{- 6}$

Step 4.3.1.2.2

Cancel the common factors.

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Step 4.3.1.2.2.1

Factor $- 2$ out of $- 6$ .

$x = - \frac{5}{6} + \frac{- 2 (y)}{- 2 (3)}$

Step 4.3.1.2.2.2

Cancel the common factor.

$x = - \frac{5}{6} + \frac{- 2 y}{- 2 \cdot 3}$

Step 4.3.1.2.2.3

Rewrite the expression.

$x = - \frac{5}{6} + \frac{y}{3}$